Your parking lights are working correctly, they don't stay on in the full on position. There is a relay that controls the dash lights. Over time the ciruit has gained enough additional series resistance to reduce the amount of current pulled through the relay. So it never fully opens. You can get anew solid state relay that will make it blink or open the one you have and very carefully bend the contacts to make it easier to actuate. (not recommended for amateurs...)

Thanks Bill. Huh, I would not have guessed that, the front parking/marker lights are not on with the headlights. Wonder why they did that?
Yeah, I read that about the relay, along with some other possibilities. Probably the relay though due to age. I'm adventurous. I'll try anything once. Took my trunk lock apart the other night, and made it match my glove box key. Those stupid little springs kept getting away from me! BTW where would I see some pictures of your lime frost car. Love that color. That's what mine is 390, 4speed, with ivy gold. Not XR7 though, and I bet yours has a vinyl top.

This is my first post. I have several questions concerning turn signals on my 68 base Cougar. First, a little background on what I have done to fix some of the electrical/light issues, what is and is not working in this area, and additional comments. I have replaced all non-working bulbs, headlight switch, brake light switch, and the fuse box. Headlights, taillights, and parking lights are working. Brake lights work only on the outside taillights. Hazard lights do not work and I have no lights (front or back) on or flashing when the turn signal indicator is placed in either right or left position. Both turn signal indicator dash lights come on in the appropriate locations with the turn signal lever but do not flash. I tested the orange/green wire going into the SQM and it has between 11V and 12V power with the turn signal lever in either left or right position. I have done no other testing in the trunk. The SQM is not running. I plan to replace all the mechanical turn signal items in the trunk with the solid state unit and this leads to my first question. Since I have power to the SQM via the orange/green wire does that mean the electronic unit should correct all my issues with turn signals and brake lights? If not what else should I test before purchasing and making the swap? I am not too concerned with the hazards at this time but this brings me to my next questions. I have 3 relays on the metal plate connected to the fuse box. Can someone validate my assumptions on these? I believe that one with 2 round posts is a circuit breaker. If so does the fact that I have power to the SQM via the orange /green wire validate that this circuit breaker is good? Is the larger oblong 3 pin connector device the turn signal relay which controls flashing of the dash turn signal indicators? Is the smaller oblong unit the emergency relay? I believe it is 2 prong. Thanks for allowing me to post and I apologize for all the questions.

Welcome abord DeNetMan.
In 1970, taillights flash from inner bulb to outer (I think was the same in 67) and if the inner bulb is not working and/or not well ground, there will be no flashing. Since you have the 4 inner bulbs not working with brakes on, I would replace them all 4 with brand new ones and I would abrade all 6 sockets & body contact surfaces to make absolutely sure that they all are well ground. That worked for me in similar circumstances, good luck.